rank reduction

On the Partial Convexification of the Low-Rank Spectral Optimization: Rank Bounds and Algorithms

  • Yongchun Li
  • Weijun Xie
    • Categories Integer Programming Tags , , , ,

    A Low-rank Spectral Optimization Problem (LSOP) minimizes a linear objective subject to multiple two-sided linear matrix inequalities intersected with a low-rank and spectral constrained domain set. Although solving LSOP is, in general, NP-hard, its partial convexification (i.e., replacing the domain set by its convex hull) termed “LSOP-R”, is often tractable and yields a high-quality solution. … Read more

    A Unified Theorem on SDP Rank Reduction

  • Anthony Man-Cho So
  • Yinyu Ye
  • Jiawei Zhang
    • Categories Approximation Algorithms, Semi-definite Programming Tags ,

    We consider the problem of finding a low-rank approximate solution to a system of linear equations in symmetric, positive semidefinite matrices. Specifically, let $A_1,\ldots,A_m \in \R^{n\times n}$ be symmetric, positive semidefinite matrices, and let $b_1,\ldots,b_m \ge 0$. We show that if there exists a symmetric, positive semidefinite matrix $X$ to the system $A_i \bullet X … Read more